Investigation of Preschool Children’s Process of Forming Basic Geometric Shapes with the Geoboard

Öz

Learning basic geometric shapes in the preschool period begins with the stages of noticing the shapes and learning their names. As children progress in the development process, they can also see the similarities and differences between shapes. Children need to learn shapes with games and concrete materials in order to be able to establish relationships between shapes and perform more complex geometry operations in the later stages. One of the tools that support the acquisition of geometric shapes is the geometry board. In the current study, the processes of children’s recognizing and forming different types of triangle, square and rectangular shapes (with different position, aspect ratio and skewness) on the geometry board were examined. Individual interviews were conducted with 24 children attending kindergarten. While the children were following the instructions given on the geometry board, observations were made and these observation notes recorded in the evaluation form were evaluated through descriptive analysis. According to the findings, children recognize these shapes and mostly use the concepts of “side-angle” when explaining their properties. It was observed that while forming the shapes on the board, they tended to form the most well-known forms of these shapes. Materials such as geometry boards are thought to be important for children for hands-on learning on a concrete material without memorizing basic geometric shapes and their properties

Anahtar Kelimeler

• Geometry in preschool
• Geoboard
• shapes
• use of materials in mathematics

Okul Öncesi Çocuklarının Geometri Tahtası İle Temel Geometrik Şekilleri Oluşturma Süreçlerinin İncelenmesi

Öz

Okul öncesi dönemde temel geometrik şekillerin öğrenilmesi ilk önce şekillerin fark edilmesi ve isimlerinin öğrenilmesi aşamaları ile başlamaktadır. Çocuklar gelişim sürecinde ilerledikçe, şekiller arasındaki benzerlik ve farklılıkları da görebilmektedirler. Çocukların sonraki aşamalarda şekiller arasında ilişki kurabilmeleri ve daha karmaşık geometri işlemlerini yapabilmeleri için, oyun ve somut materyallerle şekilleri öğrenme gereksinimleri vardır. Geometrik şekillerin kazanılmasını destekleyen araçlardan biri geometri tahtasıdır. Bu araştırmada çocukların üçgen, kare ve dikdörtgen şekillerinin farklı türdeki örneklerini (farklı konum, basıklık ve çarpıklık özelliği olan) geometri tahtası üzerinde tanıma ve oluşturma süreçleri incelenmiştir. Anasınıfına devam eden 24 çocuk ile bireysel görüşmeler yapılmıştır. Çocuklar geometri tahtası üzerinde verilen yönergeleri uygularken gözlem yapılmış ve değerlendirme formuna kaydedilen bu gözlem notları betimsel analiz değerlendirilmiştir. Elde edilen bulgulara göre, çocuklar bu şekilleri tanımakta ve özelliklerini açıklarken en çok “kenar-köşe” kavramlarını kullanmaktadır. Tahta üzerinde şekilleri oluştururken bu şekillerin en çok bilinen biçimlerini oluşturma eğiliminde oldukları görülmüştür. Temel geometrik şekilleri ve özelliklerini ezberlemeden, somut bir materyal üzerinde uygulamalı öğrenilmesi için geometri tahtası gibi materyallerin çocuklar için önemli olduğu düşünülmektedir.

Anahtar Kelimeler

• okul öncesinde geometri
• geometri tahtası
• şekiller
• matematikte materyal kullanımı

Kaynakça

1. Acharya, B. J. (2017). Factors affecting difficulties in learning mathematics by mathematics learners. International Journal of Elementary Education, 6(2), 8-15.
2. Alisinanoğlu, F., Kesicioğlu, O. S., & Mart, M. (2013). Evaluation of pre-school children’s development of geometric thought in the UK and Turkey according to van Hiele model. International Journal of Education and Research, 1(10), 1-10
3. Allen, K. (2013). The geoboard triangle quest. Mathematics Teacher, 107(2), 113–18. https://www.jstor.org/stable/10.5951/mathteacher.107.2.0112
4. Aslan, D., & Arnas, Y. A. (2007). Three‐to six‐year‐old children’s recognition of geometric shapes. International Journal of Early Years Education, 15(1), 83-104. https://doi.org/10.1080/09669760601106646
5. Balinha, F., & Mamede, E. (2018). Young children working with geometric figures. Journal of the European Teacher Education Network, 13, 11–22.
6. Canada, D., L., Ciancetta, M. A., & Blair, S. D. (2014). Going off-the-pegs: Revisiting geoboard squares. Mathematics Teaching in the Middle School, 20(5), 286-292. https://doi.org/10.5951/mathteacmiddscho.20.5.0286
7. Clements, D. H., Sarama, J., Swaminathan, S., Weber, D., & Trawick-Smith, J. (2018). Teaching and learning Geometry: early foundations. Quadrante, 27(2), 7-31.
8. Clements, D. H., & Sarama, J. (2000). Young children’s ideas about geometric shapes. Teaching Children Mathematics, 6(8), 482-488.

9. Clements, D. H., Swaminathan, S., Hannibal, M. A. Z. & Sarama, J. (1999). Young children’s concepts of shape. Journal for Research in Mathematics Education, 30, 192-212.
10. Creswell, J. W. (2016). Nitel Araştırma Yöntemleri: Beş Yaklaşıma Göre Nitel Araştırma ve Araştırma Deseni. (M. Bütün ve S. B. Demir, Çev.). Siyasal Kitabevi.
11. Dagli, Ü. Y., & Halat, E. (2016). Young Children's Conceptual Understanding of Triangle. EURASIA Journal of Mathematics, Science & Technology Education, 12(2), 189-202. https://doi.org/10.12973/eurasia.2016.1398a
12. Eason, S. H. & Ramani, G. B. (2020). Parent–child math talk about fractions during formal learning and guided play activities. Child Development, 91(2), 546-562. https://doi.org/10.1111/cdev.13199
13. Fisher, K. R., Hirsh‐Pasek, K., Newcombe, N., & Golinkoff, R. M. (2013). Taking shape: Supporting preschoolers' acquisition of geometric knowledge through guided play. Child Development, 84(6), 1872-1878. https://doi.org/10.1111/cdev.12091
14. Flevares, L. M., & Schiff, J. R. (2014). Learning mathematics in two dimensions: A review and look ahead at teaching and learning early childhood mathematics with children’s literature. Frontiers in Psychology, 5, 1-12. https://doi.org/10.3389/fpsyg.2014.00459
15. Furner, J. M., & Marinas, C. A. (2011). Geoboards to geogebra: Moving from the concrete 6 to the abstract in geometry. Retrieved from http://archives.math.utk.edu/ICTCM/vol23/S0 88/paper.pdf
16. Gejard, G., & Melander, H. (2018). Mathematizing in preschool: Children’s participation in geometrical discourse. European Early Childhood Education Research Journal, 26(4), 495-511. https://doi.org/10.1080/1350293X.2018.1487143
17. Hodzhev, Y., & Chernev, N. (2018). Open geoboard–a platform for art, math and ınspiration. In Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture (pp. 603-608).
18. Junthong, N., Netpradit, S., & Boonlue, S. (2020). The designation of geometry teaching tools for visually-impaired students using plastic geoboards created by 3D printing. The New Educational Review, 59(1), 87-102. https://doi.org/10.15804/tner.2020.59.1.07
19. Junthong, N., Netpradit, S., & Boonlue, S. (2018). Design and development of teaching tools in dimensional geometry for visually ımpaired students using object models from 3D printing. In 10 International Conference on Languages, Humanities, Education and Social Sciences. Kyoto: LHESS-18. Recuperado a partir de: http://heaig. org/images/proceedings_pdf H (Vol. 418464).
20. Kalenine, S., Pinet, L., & Gentaz, E. (2011). The visual and visuo-haptic exploration of geometrical shapes increases their recognition in preschoolers. International Journal of Behavioral Development, 35(1), 18-26. https://doi.org/10.1177/0165025410367443
21. Karademir, A. (2020). Soruşturma temelli erken geometri öğrenimine yönelik manipülatif materyaller. Erken Çocuklukta Araştıma ve Uygulamalarla Soruşturma Temelli Erken Geometri Öğrenimi içinde bölüm. Ed: H. İ. Korkmaz. Ankara: Eğiten Kitap.
22. Kesicioğlu, O. S. (2013). The effect of gender and computer use variables on recognation of geometrical shapes in preschool children. International Journal on New Trends in Education and Their Implications, 4(3), 48- 56.
23. Kesicioğlu, O. S., Alisinanoğlu, F., & Tuncer, A. T. (2011). The analysis of kindergarteners` recognition degrees of geometric shapes. Elementary Education Online, 10(2), 1093-1111. doi: 10.17051/IO.94018
24. Korkmaz, H. İ., & Tekin, B. (2020). Investigating preschool age children’s strategies of creating geometrical shapes in problem-based tasks. Kastamonu Education Journal, 28(2), 729-747. https://doi.org/10.24106/kefdergi.697203
25. Loong, Y. (2014). Fostering mathematical understanding through physical and virtual manipulatives. The Australian Mathematics Teacher, 70(4), 3-10. https://www.learntechlib.org/p/194801
26. Matengu, G. K., & Schäfer, M. (2022). Revisiting geoboards to teach quadrilaterals within the van hiele teaching framework. Book Of Proceedings–Long Papers, pp. 63-75.
27. Meagher, M. S., Edwards, M. T., & Özgün-Koca, S. A. (2016). What's your answer? Searching for triangles. The Mathematics Teacher, 109(7), 500-506. https://www.jstor.org/stable/10.5951/mathteacher.109.7.0500
28. Merriam, S. B. (2013). Nitel Araştırma: Desen ve Uygulama İçin Bir Rehber. (S. Turan, Çev. Ed.). Ankara: Nobel Yayın Dağıtım.
29. Mix, K. S. (2019). Why are spatial skill and mathematics related? Child Development Perspectives, 13, 121–126. https://doi.org/10.1111/cdep.12323
30. MoNE. (2013). Early Childhood Education Program. Ministry of National Education, Ankara. Online available from https://tegm.meb.gov.tr/dosya/okuloncesi/ooproram.pdf.
31. Musyoka, M. M. (2015). Understanding indoor play in deaf children: An analysis of play behaviors. Psychology, 6(01), 10-19. https://doi.org/10.4236/psych.2015.61002
32. National Council of Teacher of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
33. Nurnberger-Haag, J. (2017). A cautionary tale: How children’s books (Mis)teach shapes. Early Education and Development, 28(4), 415–440. https://doi.org/10.1080/10409289.2016.1242993
34. Ostad, S. A. (2020). Private speech use in mathematics problem solving: A review of studies comparing children with and without mathematical difficulties. International Journal for Research in Learning Disabilities, 4(2), 53-65. https://doi.org/10.28987/ijrld.4.2.53
35. Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri. (M. Bütün ve S. Demir Çev. Ed.). Ankara: Pegem Akademi Yayınları.
36. Rahmiati, M. (2016). The attempt to improve mathematics learning motivation using the geoboard (Spiked Board) Among Grade II Elementary School Students. Global Journal of Business and Social Science Review, 4(3), 74-78. https://doi.org/10.35609/gjbssr.2016.4.3(11)
37. Resnick, I., Verdine, B. N., Golinkoff, R., & Hirsh-Pasek, K. (2016). Geometric toys in the attic? A corpus analysis of early exposure to geometric shapes. Early Childhood Research Quarterly, 36, 358–365. https://doi.org/10.1016/j.ecresq.2016.01.007
38. Ribeiro, L. A., Casey, B., Dearing, E., Nordahl, K. B., Aguiar, C., & Zachrisson, H. (2020). Early maternal spatial support for toddlers and math skills in second grade. Journal of Cognition and Development, 21(2), 282- 311. https://doi.org/10.1080/15248372.2020.1717494
39. Sabil, H., Asrial, A., Syahrial, S., Robiansah, M. A., Zulkhi, M. D., Damayanti, L., & Ubaidillah, U. (2021). Online geoboard media in mathematics learning: Understanding the concept of two-dimentional figure. Journal of Education Technology, 6(1), 12-18. https://doi.org/10.23887/ijee.v5i4.41785
40. Sezer, T., & Güven, Y. (2019). 5-7 yaş grubu çocukların geometri becerilerinin incelenmesi. Erken Çocukluk Çalışmaları Dergisi, 3(2), 514-540, doi: 10.24130/eccd-jecs.196.720.1932187
41. Sezer, T., & Güven, Y. (2016). The Development of Early Geometry Skills Test. Atatürk University Journal of Kazım Karabekir Education Faculty, (33), 1-22. https://dergipark.org.tr/en/pub/ataunikkefd/issue/27013/284044
42. Sibiya, M. R., & Mudaly, V. (2018). The effects of the geoboard on learner understanding of geometry theorems. PONTE International Journal of Sciences and Research, 74(11/1), 90-98. https://doi.org/10.21506/j.ponte.2018.11.8
43. Sibiya, M. R. (2019). The effect of Geoboard use on learners’ motivation for learning of Geometry theorems. International Journal of Sciences and Research, 75(6), 71-85. https://doi.org/10.21506/ j.ponte.2019.6.14
44. Sibiya, M. R. (2020). A Reconsideration of the Effectiveness of Using Geoboard in Teaching Euclidean Geometry. EURASIA Journal of Mathematics, Science and Technology Education, 16(9), em1876. https://doi.org/10.29333/ejmste/8360
45. Scandrett, H. (2008). Using geoboards in primary mathematics: Going... going... gone?. Australian Primary Mathematics Classroom, 13(2), 29-32. https://files.eric.ed.gov/fulltext/EJ802704.pdf
46. Schmitt, S. A., Korucu, I., Napoli, A. R., Bryant, L. M., & Purpura, D. J. (2018). Using block play to enhance preschool children’s mathematics and executive functioning: A randomized controlled trial. Early Childhood Research Quarterly,44, 181–191. https://doi.org/10.1016/j.ecresq.2018.04.006.
47. Skoumpourdi, C. (2016). Different modes of communicating geometric shapes, through a game, in kindergarten. International Journal for Mathematics Teaching and Learning, 17(2), 1-23. http://www.cimt.org.uk/ijmtl/index.php/IJMTL/article/view/16/12
48. Skoumpourdi, C. (2013). Guess which: Shapes’ descriptions by toddlers. Proceedings of CIEAEM 65, Mathematics Education in a Globalized Environment, (CD), Torino, Italy.
49. Sperry-Smith, S. (2016). Erken Çocuklukta Matematik. (S. Erdoğan Çev. Ed.) Ankara: Eğiten Kitap.
50. Uhlířová, M. (2019). Developing mathematical thinking through educational activities on the geoboard. In Proceedings of EDULEARN19 Conference (pp. 2340-1117).
51. Van De Walle, J. A., Karp, K. S. ve Bay-Williams, J. M. (2014). İlkokul ve ortaokul matematiği gelişimsel yaklaşımla öğretim. (S. Durmuş, Çev. Ed.). Ankara: Nobel Akademik Yayıncılık.
52. Verdine, B. N., Lucca, K. R., Golinkoff, R. M., Hirsh-Pasek, K., & Newcombe, N. S. (2016). The shape of things: The origin of young children's knowledge of the names and properties of geometric forms. Journal of Cognition and Development, 17(1), 142–161. https://doi.org/10.1080/15248372.2015.1016610
53. Yıldırım, A., ve Şimşek, H. (2018). Sosyal bilimlerde nitel araştırma yöntemleri (11. basım). Ankara: Seçkin Yayıncılık. Zambrzycka, J., Kotsopoulos, D., Lee, J., & Makosz, S. (2017). In any way, shape, or form? Toddlers’ understanding of shapes. Infant Behavior and Development, 46, 144-157. https://doi.org/10.1016/j.infbeh.2016.12.002 Žilková, K., Partová, E., Kopáčová, J., Tkačik, Š., Mokriš, M., Budínová, I., & Gunčaga, J. (2018). Young Children's Concepts of Geometric Shapes. Harlow: Pearson.